<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">

<!-- 
	Copyright (C) 2007, 2008, 2009, 2010, 2011. PARP Research Group.
	<http://perception.inf.um.es>
	University of Murcia, Spain.

	This file is part of the QVision library.

	QVision is free software: you can redistribute it and/or modify
	it under the terms of the GNU Lesser General Public License as
	published by the Free Software Foundation, version 3 of the License.

	QVision is distributed in the hope that it will be useful,
	but WITHOUT ANY WARRANTY; without even the implied warranty of
	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
	GNU Lesser General Public License for more details.

	You should have received a copy of the GNU Lesser General Public
	License along with QVision. If not, see <http://www.gnu.org/licenses/>.
-->

<html><head><meta http-equiv="content-Type" content="text/html;charset=UTF-8">
<title>QVision: Qt&#39;s Image, Video and Computer Vision Library</title>
<meta name="title" content="QVision" />
<meta name="dc.title" content="QVision" />
<meta name="url" content="http://perception.inf.um.es/QVision" />
<meta name="author" content="PARP Research Group - http://perception.inf.um.es" />
<meta name="revisit-after" content="30 DAYS"/>
<meta name="robots" content="index,follow"/>
<meta name="classification" content="*">
<meta name="rating" content="Safe For Kids">
<meta name="distribution" content="GLOBAL"/>
<meta name="description" content="Qt's Image, Video and Computer Vision Library"/>
<meta name="page-topic" content="Computer Vision research and prototype programming"/>
<meta name="geo.country" content="ES" />

<!--
Keywords:
By license:		open source, gnu, lgpl, gpl, free
By theme:		computer vision, image processing, robotics, programming, source, development
By usage:		library, toolkit, framework, prototype, application
By programming specs:	object oriented, c++, block programming, reusability, gui, graphical, parallel computing, high performance, GPU, prototyping
Interoperability with:	Qt, GSL, GNU Scientific library, OpenCV, CGAL, QWT, CUDA, mplayer, IPP, Intel Image Performance Primitives, blas, lapack
Functionallity:		image features, matrix algebra, projective geometry, mser, function minimization, function optimization, canny operator, harris operator, corner detection, performance evaluation, cpu usage, graphical interface
Main data-types:	matrix, vector, tensor, quaternion, image, polyline
Video sources:		webcam, camera, stream
Devices:		embedded, desktop computer, laptop, mini-laptop
Authors:		PARP research group. University of Murcia, Spain.
-->

<meta name="keywords" content="augmented reality, sfm, structure from motion, open source, gnu, lgpl, gpl, free, computer vision, image processing, robotics, programming, source, development, library, toolkit, framework, prototype, application, object oriented, c++, block programming, reusability, gui, graphical, parallel computing, high performance, GPU, prototyping, Qt, GSL, GNU Scientific library, OpenCV, CGAL, QWT, CUDA, mplayer, IPP, Intel Image Performance Primitives, blas, lapack, image features, matrix algebra, projective geometry, mser, function minimization, function optimization, canny operator, harris operator, corner detection, performance evaluation, cpu usage, graphical interface, matrix, vector, tensor, quaternion, image, polyline, webcam, camera, stream, embedded, desktop computer, laptop, mini-laptop, University of Murcia, Spain, PARP research group, vision por computador"/>
<meta http-equiv="keywords" content="augmented reality, sfm, structure from motion, open source, gnu, lgpl, gpl, free, computer vision, image processing, robotics, programming, source, development, library, toolkit, framework, prototype, application, object oriented, c++, block programming, reusability, gui, graphical, parallel computing, high performance, GPU, prototyping, Qt, GSL, GNU Scientific library, OpenCV, CGAL, QWT, CUDA, mplayer, IPP, Intel Image Performance Primitives, blas, lapack, image features, matrix algebra, projective geometry, mser, function minimization, function optimization, canny operator, harris operator, corner detection, performance evaluation, cpu usage, graphical interface, matrix, vector, tensor, quaternion, image, polyline, webcam, camera, stream, embedded, desktop computer, laptop, mini-laptop, University of Murcia, Spain, PARP research group, vision por computador"/>
<meta http-equiv="pragma" content="no-cache"/>
<meta http-equiv="title" content="QVision"/>
<link href="doxygen.css" rel="stylesheet" type="text/css" />
<link href="tabs.css" rel="stylesheet" type="text/css" />
<link rel="shortcut icon" href="favicon.ico" />
</head><body>

<table width="100%"><tr>
	<td><a href="http://perception.inf.um.es/"><img src="parp.png" border="0" /> <big>PARP Research Group</big></a></td>
	<td align="right"><a href="http://www.um.es/"><big>Universidad de Murcia</big> <img src="um.png" border="0" /></a></td>
</tr></table>

<hr /><br />

<table width="95%" align="center"><tr><td>

<!-- Generated by Doxygen 1.6.3 -->
<script type="text/javascript"><!--
var searchBox = new SearchBox("searchBox", "search",false,'Search');
--></script>
<div class="navigation" id="top">
  <div class="tabs">
    <ul>
      <li><a href="index.html"><span>Main&nbsp;Page</span></a></li>
      <li><a href="pages.html"><span>Related&nbsp;Pages</span></a></li>
      <li><a href="modules.html"><span>Modules</span></a></li>
      <li><a href="annotated.html"><span>Classes</span></a></li>
      <li class="current"><a href="files.html"><span>Files</span></a></li>
      <li>
        <div id="MSearchBox" class="MSearchBoxInactive">
          <form id="FSearchBox" action="search.php" method="get">
            <img id="MSearchSelect" src="search/search.png" alt=""/>
            <input type="text" id="MSearchField" name="query" value="Search" size="20" accesskey="S" 
                   onfocus="searchBox.OnSearchFieldFocus(true)" 
                   onblur="searchBox.OnSearchFieldFocus(false)"/>
          </form>
        </div>
      </li>
    </ul>
  </div>
  <div class="tabs">
    <ul>
      <li><a href="files.html"><span>File&nbsp;List</span></a></li>
      <li><a href="globals.html"><span>File&nbsp;Members</span></a></li>
    </ul>
  </div>
<h1>src/qvmath/qvquaternion.cpp</h1><a href="qvquaternion_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">/*</span>
<a name="l00002"></a>00002 <span class="comment"> *      Copyright (C) 2007, 2008, 2009, 2010, 2011, 2012. PARP Research Group.</span>
<a name="l00003"></a>00003 <span class="comment"> *      &lt;http://perception.inf.um.es&gt;</span>
<a name="l00004"></a>00004 <span class="comment"> *      University of Murcia, Spain.</span>
<a name="l00005"></a>00005 <span class="comment"> *</span>
<a name="l00006"></a>00006 <span class="comment"> *      This file is part of the QVision library.</span>
<a name="l00007"></a>00007 <span class="comment"> *</span>
<a name="l00008"></a>00008 <span class="comment"> *      QVision is free software: you can redistribute it and/or modify</span>
<a name="l00009"></a>00009 <span class="comment"> *      it under the terms of the GNU Lesser General Public License as</span>
<a name="l00010"></a>00010 <span class="comment"> *      published by the Free Software Foundation, version 3 of the License.</span>
<a name="l00011"></a>00011 <span class="comment"> *</span>
<a name="l00012"></a>00012 <span class="comment"> *      QVision is distributed in the hope that it will be useful,</span>
<a name="l00013"></a>00013 <span class="comment"> *      but WITHOUT ANY WARRANTY; without even the implied warranty of</span>
<a name="l00014"></a>00014 <span class="comment"> *      MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the</span>
<a name="l00015"></a>00015 <span class="comment"> *      GNU Lesser General Public License for more details.</span>
<a name="l00016"></a>00016 <span class="comment"> *</span>
<a name="l00017"></a>00017 <span class="comment"> *      You should have received a copy of the GNU Lesser General Public</span>
<a name="l00018"></a>00018 <span class="comment"> *      License along with QVision. If not, see &lt;http://www.gnu.org/licenses/&gt;.</span>
<a name="l00019"></a>00019 <span class="comment"> */</span>
<a name="l00020"></a>00020 
<a name="l00024"></a>00024 
<a name="l00025"></a>00025 <span class="preprocessor">#include &lt;QString&gt;</span>
<a name="l00026"></a>00026 <span class="preprocessor">#include &lt;QVMatrix&gt;</span>
<a name="l00027"></a>00027 <span class="preprocessor">#include &lt;QVQuaternion&gt;</span>
<a name="l00028"></a>00028 <span class="preprocessor">#include &lt;qvmath.h&gt;</span>
<a name="l00029"></a>00029 
<a name="l00031"></a>00031 <span class="comment">// Constructors</span>
<a name="l00032"></a><a class="code" href="classQVQuaternion.html#a7475a2c805849a356b5829a5595c536b">00032</a> <a class="code" href="classQVQuaternion.html#a7475a2c805849a356b5829a5595c536b" title="Identity constructor.">QVQuaternion::QVQuaternion</a>(): <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a>(4)
<a name="l00033"></a>00033         {
<a name="l00034"></a>00034         <span class="keyword">set</span>(0);
<a name="l00035"></a>00035         operator[](3) = 1;
<a name="l00036"></a>00036         Q_ASSERT(<a class="code" href="classQVQuaternion.html#ac7a9049ab48eb43f9ed7ddae01b3126a" title="Gets the norm2 of the quaternion.">norm2</a>() &gt; 0);
<a name="l00037"></a>00037         }
<a name="l00038"></a>00038 
<a name="l00039"></a><a class="code" href="classQVQuaternion.html#a9ee4bf11cb29232be2cef660fd0aacd6">00039</a> <a class="code" href="classQVQuaternion.html#a7475a2c805849a356b5829a5595c536b" title="Identity constructor.">QVQuaternion::QVQuaternion</a>(<span class="keyword">const</span> <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> a, <span class="keyword">const</span> <span class="keywordtype">double</span> phi):<a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a>(4)
<a name="l00040"></a>00040         {
<a name="l00041"></a>00041         <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> a_normal = a * (sin(phi/2.0) / a.<a class="code" href="classQVVector.html#a49c6f41f1fa80efcc943f1c26fdcbf05" title="Norm 2 of the vector.">norm2</a>());
<a name="l00042"></a>00042 
<a name="l00043"></a>00043         operator[](0) = a_normal[0];
<a name="l00044"></a>00044         operator[](1) = a_normal[1];
<a name="l00045"></a>00045         operator[](2) = a_normal[2];
<a name="l00046"></a>00046         operator[](3) = cos(phi/2.0);
<a name="l00047"></a>00047 
<a name="l00048"></a>00048         Q_WARNING(not <a class="code" href="classQVVector.html#a29235517605f49f2327df62d5e0295df" title="Checks whether the vector contains a NaN value or not.">containsNaN</a>());
<a name="l00049"></a>00049         Q_ASSERT(<a class="code" href="classQVQuaternion.html#ac7a9049ab48eb43f9ed7ddae01b3126a" title="Gets the norm2 of the quaternion.">norm2</a>() &gt; 0);
<a name="l00050"></a>00050         }
<a name="l00051"></a>00051 
<a name="l00052"></a><a class="code" href="classQVQuaternion.html#ab5c7e55c31b8523d74fae84889a96ce4">00052</a> <a class="code" href="classQVQuaternion.html#a7475a2c805849a356b5829a5595c536b" title="Identity constructor.">QVQuaternion::QVQuaternion</a>(<span class="keyword">const</span> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> &amp;R): <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a>(4)
<a name="l00053"></a>00053         {
<a name="l00054"></a>00054         Q_ASSERT(not R.<a class="code" href="classQVMatrix.html#a43455dfaf2e8fa71242ea1fdc8beb102" title="Checks whether the matrix contains a NaN value or not.">containsNaN</a>());
<a name="l00055"></a>00055         Q_ASSERT(R.<a class="code" href="classQVMatrix.html#a387750529622104faba8047cb0efa62a" title="Gets the norm2 for matrix.">norm2</a>() &gt; 0);
<a name="l00056"></a>00056 
<a name="l00057"></a>00057         <span class="keywordtype">int</span> u, v, w;
<a name="l00058"></a>00058 
<a name="l00059"></a>00059         <span class="comment">// Sort the elements of the trace of Q.</span>
<a name="l00060"></a>00060         <span class="keywordflow">if</span> (R(0,0) &gt; R(1,1))
<a name="l00061"></a>00061                 <span class="keywordflow">if</span> (R(0,0) &gt; R(2,2))
<a name="l00062"></a>00062                         <span class="keywordflow">if</span> (R(1,1) &gt; R(2,2))
<a name="l00063"></a>00063                                 { u = 0; v = 1; w = 2; }
<a name="l00064"></a>00064                         <span class="keywordflow">else</span>
<a name="l00065"></a>00065                                 { u = 0; v = 2; w = 1; }
<a name="l00066"></a>00066                 <span class="keywordflow">else</span>
<a name="l00067"></a>00067                         <span class="keywordflow">if</span> (R(0,0) &gt; R(2,2))
<a name="l00068"></a>00068                                 { u = 1; v = 0; w = 2; }
<a name="l00069"></a>00069                         <span class="keywordflow">else</span>
<a name="l00070"></a>00070                                 { u = 1; v = 2; w = 0; }
<a name="l00071"></a>00071         <span class="keywordflow">else</span>
<a name="l00072"></a>00072                 <span class="keywordflow">if</span> (R(1,1) &gt; R(2,2))
<a name="l00073"></a>00073                         <span class="keywordflow">if</span> (R(0,0) &gt; R(2,2))
<a name="l00074"></a>00074                                 { u = 1; v = 0; w = 2; }
<a name="l00075"></a>00075                         <span class="keywordflow">else</span>
<a name="l00076"></a>00076                                 { u = 1; v = 2; w = 0; }
<a name="l00077"></a>00077                 <span class="keywordflow">else</span>
<a name="l00078"></a>00078                         <span class="keywordflow">if</span> (R(0,0) &gt; R(1,1))
<a name="l00079"></a>00079                                 { u = 2; v = 0; w = 1; }
<a name="l00080"></a>00080                         <span class="keywordflow">else</span>
<a name="l00081"></a>00081                                 { u = 2; v = 1; w = 0; }
<a name="l00082"></a>00082 
<a name="l00083"></a>00083         Q_ASSERT(u != v);
<a name="l00084"></a>00084         Q_ASSERT(v != w);
<a name="l00085"></a>00085         Q_ASSERT(u != w);
<a name="l00086"></a>00086 
<a name="l00087"></a>00087         <span class="keywordflow">if</span> (1.0 + R(u,u) - R(v,v) - R(w,w) &lt; 0.0)
<a name="l00088"></a>00088                 {
<a name="l00089"></a>00089                 *<span class="keyword">this</span> = <a class="code" href="classQVQuaternion.html#a7475a2c805849a356b5829a5595c536b" title="Identity constructor.">QVQuaternion</a>(-R);
<a name="l00090"></a>00090                 <span class="keywordflow">return</span>;
<a name="l00091"></a>00091                 }
<a name="l00092"></a>00092 
<a name="l00093"></a>00093         Q_ASSERT(1.0 &gt;= - R(u,u) + R(v,v) + R(w,w));
<a name="l00094"></a>00094         <span class="keyword">const</span> <span class="keywordtype">double</span> r = sqrt(1.0 + R(u,u) - R(v,v) - R(w,w));
<a name="l00095"></a>00095 
<a name="l00096"></a>00096         <span class="comment">// Estimate the values of the quaternion</span>
<a name="l00097"></a>00097         <span class="keywordflow">if</span> (ABS(r) &lt; 1e-100)
<a name="l00098"></a>00098                 {
<a name="l00099"></a>00099                 operator[](u) = 0.0; 
<a name="l00100"></a>00100                 operator[](v) = 0.0;
<a name="l00101"></a>00101                 operator[](w) = 0.0;
<a name="l00102"></a>00102                 operator[](3) = 1.0;
<a name="l00103"></a>00103                 }
<a name="l00104"></a>00104         <span class="keywordflow">else</span>    {
<a name="l00105"></a>00105                 operator[](u) = r / 2.0; 
<a name="l00106"></a>00106                 operator[](v) = (R(u,v) + R(v,u)) / (2.0*r);
<a name="l00107"></a>00107                 operator[](w) = (R(u,w) + R(w,u)) / (2.0*r);
<a name="l00108"></a>00108                 operator[](3) = (R(w,v) - R(v,w)) / (2.0*r);
<a name="l00109"></a>00109                 }
<a name="l00110"></a>00110 
<a name="l00111"></a>00111         Q_WARNING(not isnan(<a class="code" href="classQVQuaternion.html#a4b71d76116709c6a6d1872bd1f137c9e" title="Returns the coordinate for the real component of the cuaternion.">real</a>()));
<a name="l00112"></a>00112         Q_WARNING(not isnan(<a class="code" href="classQVQuaternion.html#aebb9e948cd7fa6e1b60e4a27f573167d" title="Returns the coordinate i of the cuaternion.">i</a>()));
<a name="l00113"></a>00113         Q_WARNING(not isnan(<a class="code" href="classQVQuaternion.html#adad1a0e10ae3d3413fe96b59ef103d26" title="Returns the coordinate j of the cuaternion.">j</a>()));
<a name="l00114"></a>00114         Q_WARNING(not isnan(<a class="code" href="classQVQuaternion.html#ae7f769c05a5ba57ec0d776d88741eeae" title="Returns the coordinate k of the cuaternion.">k</a>()));
<a name="l00115"></a>00115 
<a name="l00116"></a>00116         <span class="comment">// Obtain correct sign for &#39;w&#39;. Knowing:</span>
<a name="l00117"></a>00117         <span class="comment">//      R(2,1) - R(1,2) == 4*x*w</span>
<a name="l00118"></a>00118         <span class="comment">// We know that:</span>
<a name="l00119"></a>00119         <span class="comment">//      SIGN(R(2,1) - R(1,2)) == SIGN(4*x*w)</span>
<a name="l00120"></a>00120         <span class="comment">// thus</span>
<a name="l00121"></a>00121         <span class="comment">//      (R(2,1) - R(1,2))*x*w &gt; 0;</span>
<a name="l00122"></a>00122         <span class="keywordflow">switch</span>(u)
<a name="l00123"></a>00123                 {
<a name="l00124"></a>00124                 <span class="comment">// R(2,1) - R(1,2) == 4*x*w     &lt;=&gt;     (R(2,1) - R(1,2))*x*w &gt; 0;</span>
<a name="l00125"></a>00125                 <span class="keywordflow">case</span> 0: <span class="keywordflow">if</span> ( (R(2,1) - R(1,2))*<span class="keyword">operator</span>[](0)*<span class="keyword">operator</span>[](3) &lt; 0)
<a name="l00126"></a>00126                                 operator[](3) = -operator[](3);
<a name="l00127"></a>00127                         <span class="keywordflow">break</span>;
<a name="l00128"></a>00128 
<a name="l00129"></a>00129                 <span class="comment">// R(0,2) - R(2,0) == 4*y*w     &lt;=&gt;     (R(0,2) - R(2,0))*y*w &gt; 0;</span>
<a name="l00130"></a>00130                 <span class="keywordflow">case</span> 1: <span class="keywordflow">if</span> ( (R(0,2) - R(2,0))*<span class="keyword">operator</span>[](1)*<span class="keyword">operator</span>[](3) &lt; 0)
<a name="l00131"></a>00131                                 operator[](3) = -operator[](3);
<a name="l00132"></a>00132                         <span class="keywordflow">break</span>;
<a name="l00133"></a>00133 
<a name="l00134"></a>00134                 <span class="comment">// R(1,0) - R(0,1) == 4*z*w     &lt;=&gt;     (R(1,0) - R(0,1))*z*w &gt; 0;</span>
<a name="l00135"></a>00135                 <span class="keywordflow">case</span> 2: <span class="keywordflow">if</span> ( (R(1,0) - R(0,1))*<span class="keyword">operator</span>[](2)*<span class="keyword">operator</span>[](3) &lt; 0)
<a name="l00136"></a>00136                                 operator[](3) = -operator[](3);
<a name="l00137"></a>00137                         <span class="keywordflow">break</span>;
<a name="l00138"></a>00138 
<a name="l00139"></a>00139                 <span class="keywordflow">default</span>:
<a name="l00140"></a>00140                         <span class="keywordflow">break</span>;
<a name="l00141"></a>00141                 }
<a name="l00142"></a>00142 
<a name="l00143"></a>00143         Q_ASSERT(not <a class="code" href="classQVVector.html#a29235517605f49f2327df62d5e0295df" title="Checks whether the vector contains a NaN value or not.">containsNaN</a>());
<a name="l00144"></a>00144         Q_ASSERT(<a class="code" href="classQVQuaternion.html#ac7a9049ab48eb43f9ed7ddae01b3126a" title="Gets the norm2 of the quaternion.">norm2</a>() &gt; 0);
<a name="l00145"></a>00145         }
<a name="l00146"></a>00146 
<a name="l00147"></a><a class="code" href="classQVQuaternion.html#a167ab4825465615d392e80ea397e7165">00147</a> <a class="code" href="classQVQuaternion.html#a7475a2c805849a356b5829a5595c536b" title="Identity constructor.">QVQuaternion::QVQuaternion</a>(<span class="keyword">const</span> <span class="keywordtype">double</span> i, <span class="keyword">const</span> <span class="keywordtype">double</span> j, <span class="keyword">const</span> <span class="keywordtype">double</span> k, <span class="keyword">const</span> <span class="keywordtype">double</span> r): <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a>(4)
<a name="l00148"></a>00148         {
<a name="l00149"></a>00149         operator[](0) = i;
<a name="l00150"></a>00150         operator[](1) = j;
<a name="l00151"></a>00151         operator[](2) = k;
<a name="l00152"></a>00152         operator[](3) = r;
<a name="l00153"></a>00153 
<a name="l00154"></a>00154         Q_WARNING(not <a class="code" href="classQVVector.html#a29235517605f49f2327df62d5e0295df" title="Checks whether the vector contains a NaN value or not.">containsNaN</a>());
<a name="l00155"></a>00155         Q_ASSERT(<a class="code" href="classQVQuaternion.html#ac7a9049ab48eb43f9ed7ddae01b3126a" title="Gets the norm2 of the quaternion.">norm2</a>() &gt; 0);
<a name="l00156"></a>00156         }
<a name="l00157"></a>00157 
<a name="l00158"></a><a class="code" href="classQVQuaternion.html#a3a5402f9367e97d887d39ce90373c1b3">00158</a> <a class="code" href="classQVQuaternion.html#a7475a2c805849a356b5829a5595c536b" title="Identity constructor.">QVQuaternion::QVQuaternion</a>(<span class="keyword">const</span> <span class="keywordtype">double</span> xAngle, <span class="keyword">const</span> <span class="keywordtype">double</span> yAngle, <span class="keyword">const</span> <span class="keywordtype">double</span> zAngle): <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a>(4)
<a name="l00159"></a>00159         {
<a name="l00160"></a>00160         <span class="keyword">const</span> <span class="keywordtype">double</span>    sinX = sinf(0.5*xAngle),
<a name="l00161"></a>00161                         sinY = sinf(0.5*yAngle),
<a name="l00162"></a>00162                         sinZ = sinf(0.5*zAngle),
<a name="l00163"></a>00163                         cosX = cosf(0.5*xAngle),
<a name="l00164"></a>00164                         cosY = cosf(0.5*yAngle),
<a name="l00165"></a>00165                         cosZ = cosf(0.5*zAngle);
<a name="l00166"></a>00166 
<a name="l00167"></a>00167         <span class="comment">// and now compute quaternion</span>
<a name="l00168"></a>00168         operator[](0) = cosZ*cosY*sinX - sinZ*sinY*cosX;
<a name="l00169"></a>00169         operator[](1) = cosZ*sinY*cosX + sinZ*cosY*sinX;
<a name="l00170"></a>00170         operator[](2) = sinZ*cosY*cosX - cosZ*sinY*sinX;
<a name="l00171"></a>00171         operator[](3) = cosZ*cosY*cosX + sinZ*sinY*sinX;
<a name="l00172"></a>00172 
<a name="l00173"></a>00173         Q_WARNING(not <a class="code" href="classQVVector.html#a29235517605f49f2327df62d5e0295df" title="Checks whether the vector contains a NaN value or not.">containsNaN</a>());
<a name="l00174"></a>00174         Q_ASSERT(<a class="code" href="classQVQuaternion.html#ac7a9049ab48eb43f9ed7ddae01b3126a" title="Gets the norm2 of the quaternion.">norm2</a>() &gt; 0);
<a name="l00175"></a>00175         }
<a name="l00176"></a>00176 
<a name="l00178"></a>00178 
<a name="l00179"></a>00179 <span class="preprocessor">#define TRACKBALLSIZE  (0.8)</span>
<a name="l00180"></a>00180 <span class="preprocessor"></span><span class="keywordtype">float</span> pixelToSphere(<span class="keyword">const</span> <span class="keywordtype">float</span> r, <span class="keyword">const</span> <span class="keywordtype">float</span> x, <span class="keyword">const</span> <span class="keywordtype">float</span> y)
<a name="l00181"></a>00181         {
<a name="l00182"></a>00182         <span class="keywordtype">float</span> d = sqrt(x*x + y*y);
<a name="l00183"></a>00183         <span class="keywordflow">return</span> (d &lt; r * 0.70710678118654752440)? sqrt(r*r - d*d) : r*r / (2*d);
<a name="l00184"></a>00184         }
<a name="l00185"></a>00185 
<a name="l00186"></a><a class="code" href="classQVQuaternion.html#afc059199578068271288acb8712cb083">00186</a> <a class="code" href="classQVQuaternion.html" title="Implementation of quaternions.">QVQuaternion</a> <a class="code" href="classQVQuaternion.html#afc059199578068271288acb8712cb083" title="Gets the quaternion corresponding to a trackball rotation.">QVQuaternion::trackball</a>(<span class="keyword">const</span> <span class="keywordtype">float</span> p1x, <span class="keyword">const</span> <span class="keywordtype">float</span> p1y, <span class="keyword">const</span> <span class="keywordtype">float</span> p2x, <span class="keyword">const</span> <span class="keywordtype">float</span> p2y)
<a name="l00187"></a>00187         {
<a name="l00188"></a>00188         <span class="comment">// Zero rotation</span>
<a name="l00189"></a>00189         <span class="keywordflow">if</span> (p1x == p2x &amp;&amp; p1y == p2y)
<a name="l00190"></a>00190                 <span class="keywordflow">return</span> <a class="code" href="classQVQuaternion.html#a7475a2c805849a356b5829a5595c536b" title="Identity constructor.">QVQuaternion</a>();
<a name="l00191"></a>00191         
<a name="l00192"></a>00192         <span class="comment">// First, figure out z-coordinates for projection of P1 and P2 to deformed sphere</span>
<a name="l00193"></a>00193         <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> p1(3), p2(3);
<a name="l00194"></a>00194         p1[0] = p1x, p1[1] = p1y, p1[2] = pixelToSphere(TRACKBALLSIZE,p1x,p1y);
<a name="l00195"></a>00195         p2[0] = p2x, p2[1] = p2y, p2[2] = pixelToSphere(TRACKBALLSIZE,p2x,p2y);
<a name="l00196"></a>00196 
<a name="l00197"></a>00197         <span class="comment">// Figure out how much to rotate around that axis.</span>
<a name="l00198"></a>00198         <span class="keywordtype">float</span> t = (p1 - p2).<a class="code" href="classQVQuaternion.html#ac7a9049ab48eb43f9ed7ddae01b3126a" title="Gets the norm2 of the quaternion.">norm2</a>() / (2.0*TRACKBALLSIZE);
<a name="l00199"></a>00199         
<a name="l00200"></a>00200         <span class="comment">// Avoid problems with out-of-control values...</span>
<a name="l00201"></a>00201         <span class="keywordflow">if</span> (t &gt; 1.0) t = 1.0;
<a name="l00202"></a>00202         <span class="keywordflow">if</span> (t &lt; -1.0) t = -1.0;
<a name="l00203"></a>00203 
<a name="l00204"></a>00204         <span class="keywordflow">return</span> <a class="code" href="classQVQuaternion.html#a7475a2c805849a356b5829a5595c536b" title="Identity constructor.">QVQuaternion</a>(p2 ^ p1, 2.0 * asin(t));                    
<a name="l00205"></a>00205         }
<a name="l00206"></a>00206 
<a name="l00207"></a><a class="code" href="classQVQuaternion.html#a60343e6be165f7022ffc852a97d791c9">00207</a> <a class="code" href="classQVQuaternion.html" title="Implementation of quaternions.">QVQuaternion</a> <a class="code" href="classQVQuaternion.html#a60343e6be165f7022ffc852a97d791c9" title="Retuns a normalized quaternion.">QVQuaternion::normalizeQuaternion</a>()<span class="keyword"> const</span>
<a name="l00208"></a>00208 <span class="keyword">        </span>{
<a name="l00209"></a>00209         <a class="code" href="classQVQuaternion.html" title="Implementation of quaternions.">QVQuaternion</a> q = *<span class="keyword">this</span>;
<a name="l00210"></a>00210 
<a name="l00211"></a>00211         <span class="keywordtype">double</span> size = q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3];
<a name="l00212"></a>00212         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> <a class="code" href="classQVQuaternion.html#aebb9e948cd7fa6e1b60e4a27f573167d" title="Returns the coordinate i of the cuaternion.">i</a> = 0; <a class="code" href="classQVQuaternion.html#aebb9e948cd7fa6e1b60e4a27f573167d" title="Returns the coordinate i of the cuaternion.">i</a> &lt; 4; <a class="code" href="classQVQuaternion.html#aebb9e948cd7fa6e1b60e4a27f573167d" title="Returns the coordinate i of the cuaternion.">i</a>++)
<a name="l00213"></a>00213                 q[<a class="code" href="classQVQuaternion.html#aebb9e948cd7fa6e1b60e4a27f573167d" title="Returns the coordinate i of the cuaternion.">i</a>] /= size;
<a name="l00214"></a>00214 
<a name="l00215"></a>00215         <span class="keywordflow">return</span> q;
<a name="l00216"></a>00216         }
<a name="l00217"></a>00217 
<a name="l00218"></a><a class="code" href="classQVQuaternion.html#ad6537490c23f56408af1db33b3f20d93">00218</a> <a class="code" href="classQVQuaternion.html" title="Implementation of quaternions.">QVQuaternion</a> <a class="code" href="classQVQuaternion.html#ad6537490c23f56408af1db33b3f20d93" title="Combination operation for quaternions.">QVQuaternion::quaternionProduct</a>(<span class="keyword">const</span> <a class="code" href="classQVQuaternion.html" title="Implementation of quaternions.">QVQuaternion</a> &amp;other)<span class="keyword"> const</span>
<a name="l00219"></a>00219 <span class="keyword">        </span>{
<a name="l00220"></a>00220         <span class="keyword">const</span> <span class="keywordtype">double</span>    x = operator[](0),      y = operator[](1),      z = operator[](2),      w = operator[](3),
<a name="l00221"></a>00221                         other_x = other[0],     other_y = other[1],     other_z = other[2],     other_w = other[3];
<a name="l00222"></a>00222 
<a name="l00223"></a>00223         <span class="keyword">const</span> <a class="code" href="classQVQuaternion.html" title="Implementation of quaternions.">QVQuaternion</a> result(      w * other_x + x * other_w + y * other_z - z * other_y,
<a name="l00224"></a>00224                                                                 w * other_y + y * other_w + z * other_x - x * other_z,
<a name="l00225"></a>00225                                                                 w * other_z + z * other_w + x * other_y - y * other_x,
<a name="l00226"></a>00226                                                                 w * other_w - x * other_x - y * other_y - z * other_z);
<a name="l00227"></a>00227 
<a name="l00228"></a>00228         Q_WARNING(not result.<a class="code" href="classQVVector.html#a29235517605f49f2327df62d5e0295df" title="Checks whether the vector contains a NaN value or not.">containsNaN</a>());
<a name="l00229"></a>00229         Q_ASSERT(result.<a class="code" href="classQVQuaternion.html#ac7a9049ab48eb43f9ed7ddae01b3126a" title="Gets the norm2 of the quaternion.">norm2</a>() &gt; 0);
<a name="l00230"></a>00230 
<a name="l00231"></a>00231         <span class="keywordflow">return</span> result;
<a name="l00232"></a>00232         }
<a name="l00233"></a>00233 
<a name="l00234"></a><a class="code" href="classQVQuaternion.html#aeb4178065e8ff7ac908d5573869d826a">00234</a> <span class="keywordtype">void</span> <a class="code" href="classQVQuaternion.html#aeb4178065e8ff7ac908d5573869d826a" title="Gets the Euler angles corresponding to the Quaternion.">QVQuaternion::toEulerAngles</a>(<span class="keywordtype">double</span> &amp;xAngle, <span class="keywordtype">double</span> &amp;yAngle, <span class="keywordtype">double</span> &amp;zAngle)<span class="keyword"> const</span>
<a name="l00235"></a>00235 <span class="keyword">        </span>{
<a name="l00236"></a>00236         Q_WARNING(not <a class="code" href="classQVVector.html#a29235517605f49f2327df62d5e0295df" title="Checks whether the vector contains a NaN value or not.">containsNaN</a>());
<a name="l00237"></a>00237         Q_ASSERT(<a class="code" href="classQVQuaternion.html#ac7a9049ab48eb43f9ed7ddae01b3126a" title="Gets the norm2 of the quaternion.">norm2</a>() &gt; 0);
<a name="l00238"></a>00238 
<a name="l00239"></a>00239         <span class="keyword">const</span> <span class="keywordtype">double</span>    s = operator[](3),
<a name="l00240"></a>00240                         x = operator[](0),
<a name="l00241"></a>00241                         y = operator[](1),
<a name="l00242"></a>00242                         z = operator[](2),
<a name="l00243"></a>00243                         sqw = s*s,
<a name="l00244"></a>00244                         sqx = x*x,
<a name="l00245"></a>00245                         sqy = y*y,
<a name="l00246"></a>00246                         sqz = z*z;
<a name="l00247"></a>00247 
<a name="l00248"></a>00248         xAngle = atan2f(2.f * (x*y + z*s), sqx - sqy - sqz + sqw);
<a name="l00249"></a>00249         yAngle = asinf(-2.f * (x*z - y*s));
<a name="l00250"></a>00250         zAngle = atan2f(2.f * (y*z + x*s), -sqx - sqy + sqz + sqw);
<a name="l00251"></a>00251         }
<a name="l00252"></a>00252 
<a name="l00253"></a><a class="code" href="classQVQuaternion.html#a00c343b8018cfc98536b13ff31341751">00253</a> <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> <a class="code" href="classQVQuaternion.html#a00c343b8018cfc98536b13ff31341751" title="Gets the rotation matrix corresponding to the Quaternion.">QVQuaternion::toRotationMatrix</a>()<span class="keyword"> const</span>
<a name="l00254"></a>00254 <span class="keyword">        </span>{
<a name="l00255"></a>00255         Q_WARNING(not <a class="code" href="classQVVector.html#a29235517605f49f2327df62d5e0295df" title="Checks whether the vector contains a NaN value or not.">containsNaN</a>());
<a name="l00256"></a>00256         Q_ASSERT(<a class="code" href="classQVQuaternion.html#ac7a9049ab48eb43f9ed7ddae01b3126a" title="Gets the norm2 of the quaternion.">norm2</a>() &gt; 0);
<a name="l00257"></a>00257 
<a name="l00258"></a>00258         <span class="keyword">const</span> <span class="keywordtype">double</span>    norm = <a class="code" href="classQVQuaternion.html#ac7a9049ab48eb43f9ed7ddae01b3126a" title="Gets the norm2 of the quaternion.">norm2</a>(),
<a name="l00259"></a>00259                         x = operator[](0) / norm,
<a name="l00260"></a>00260                         y = operator[](1) / norm,
<a name="l00261"></a>00261                         z = operator[](2) / norm,
<a name="l00262"></a>00262                         w = operator[](3) / norm;
<a name="l00263"></a>00263 
<a name="l00264"></a>00264         <a class="code" href="classQVMatrix.html" title="Implementation of numerical matrices.">QVMatrix</a> result(3,3);
<a name="l00265"></a>00265         result(0,0) = 1.0 - 2.0 * (y*y + z*z);
<a name="l00266"></a>00266         result(0,1) = 2.0 * (x*y - z*w);
<a name="l00267"></a>00267         result(0,2) = 2.0 * (z*x + y*w);
<a name="l00268"></a>00268         
<a name="l00269"></a>00269         result(1,0) = 2.0 * (x*y + z*w);
<a name="l00270"></a>00270         result(1,1) = 1.0 - 2.0 * (z*z + x*x);
<a name="l00271"></a>00271         result(1,2) = 2.0 * (y*z - x*w);
<a name="l00272"></a>00272         
<a name="l00273"></a>00273         result(2,0) = 2.0 * (z*x - y*w);
<a name="l00274"></a>00274         result(2,1) = 2.0 * (y*z + x*w);
<a name="l00275"></a>00275         result(2,2) = 1.0 - 2.0 * (y*y + x*x);
<a name="l00276"></a>00276 
<a name="l00277"></a>00277         <span class="keywordflow">return</span> result;
<a name="l00278"></a>00278         }
<a name="l00279"></a>00279 
<a name="l00280"></a><a class="code" href="classQVQuaternion.html#abce39f61e6deb9ca1fdab9a3745c0383">00280</a> <a class="code" href="classQVQuaternion.html" title="Implementation of quaternions.">QVQuaternion</a> <a class="code" href="classQVQuaternion.html#abce39f61e6deb9ca1fdab9a3745c0383" title="Gets the conjugate of the quaternion.">QVQuaternion::conjugate</a>()<span class="keyword"> const</span>
<a name="l00281"></a>00281 <span class="keyword">        </span>{
<a name="l00282"></a>00282         <span class="keyword">const</span> <a class="code" href="classQVQuaternion.html" title="Implementation of quaternions.">QVQuaternion</a> result(-<span class="keyword">operator</span>[](0), -<span class="keyword">operator</span>[](1), -<span class="keyword">operator</span>[](2), <span class="keyword">operator</span>[](3));
<a name="l00283"></a>00283 
<a name="l00284"></a>00284         Q_WARNING(not result.<a class="code" href="classQVVector.html#a29235517605f49f2327df62d5e0295df" title="Checks whether the vector contains a NaN value or not.">containsNaN</a>());
<a name="l00285"></a>00285         Q_ASSERT(result.<a class="code" href="classQVQuaternion.html#ac7a9049ab48eb43f9ed7ddae01b3126a" title="Gets the norm2 of the quaternion.">norm2</a>() &gt; 0);
<a name="l00286"></a>00286 
<a name="l00287"></a>00287         <span class="keywordflow">return</span> result;
<a name="l00288"></a>00288         }
<a name="l00289"></a>00289 
<a name="l00290"></a><a class="code" href="classQVQuaternion.html#a50fdd28714a4034db3ba71dbd0a3af7f">00290</a> <a class="code" href="classQVQuaternion.html" title="Implementation of quaternions.">QVQuaternion</a> <a class="code" href="classQVQuaternion.html#a50fdd28714a4034db3ba71dbd0a3af7f" title="Gets the inverse of the quaternion.">QVQuaternion::inverse</a>()<span class="keyword"> const</span>
<a name="l00291"></a>00291 <span class="keyword">        </span>{
<a name="l00292"></a>00292         Q_ASSERT(<a class="code" href="classQVQuaternion.html#ac7a9049ab48eb43f9ed7ddae01b3126a" title="Gets the norm2 of the quaternion.">norm2</a>() &gt; 0);
<a name="l00293"></a>00293 
<a name="l00294"></a>00294         <span class="keyword">const</span> <a class="code" href="classQVQuaternion.html" title="Implementation of quaternions.">QVQuaternion</a> result = <a class="code" href="classQVQuaternion.html#abce39f61e6deb9ca1fdab9a3745c0383" title="Gets the conjugate of the quaternion.">conjugate</a>();
<a name="l00295"></a>00295 
<a name="l00296"></a>00296         Q_WARNING(not result.<a class="code" href="classQVVector.html#a29235517605f49f2327df62d5e0295df" title="Checks whether the vector contains a NaN value or not.">containsNaN</a>());
<a name="l00297"></a>00297         Q_ASSERT(result.<a class="code" href="classQVQuaternion.html#ac7a9049ab48eb43f9ed7ddae01b3126a" title="Gets the norm2 of the quaternion.">norm2</a>() &gt; 0);
<a name="l00298"></a>00298 
<a name="l00299"></a>00299         <span class="keywordflow">return</span> result / result.<a class="code" href="classQVQuaternion.html#ac7a9049ab48eb43f9ed7ddae01b3126a" title="Gets the norm2 of the quaternion.">norm2</a>();
<a name="l00300"></a>00300         }
<a name="l00301"></a>00301 
<a name="l00302"></a><a class="code" href="classQVQuaternion.html#ac7a9049ab48eb43f9ed7ddae01b3126a">00302</a> <span class="keywordtype">double</span> <a class="code" href="classQVQuaternion.html#ac7a9049ab48eb43f9ed7ddae01b3126a" title="Gets the norm2 of the quaternion.">QVQuaternion::norm2</a>()<span class="keyword"> const</span>
<a name="l00303"></a>00303 <span class="keyword">        </span>{
<a name="l00304"></a>00304         <span class="keywordflow">return</span> <a class="code" href="classQVQuaternion.html#ac7a9049ab48eb43f9ed7ddae01b3126a" title="Gets the norm2 of the quaternion.">QVVector::norm2</a>();
<a name="l00305"></a>00305         }
<a name="l00306"></a>00306 
<a name="l00307"></a><a class="code" href="classQVQuaternion.html#ad93f718564df9914bc11d2e893fcba3c">00307</a> <a class="code" href="classQV3DPointF.html" title="3D point representation">QV3DPointF</a> <a class="code" href="classQVQuaternion.html#ad93f718564df9914bc11d2e893fcba3c" title="Direct vector rotation.">QVQuaternion::rotate</a>(<span class="keyword">const</span> <a class="code" href="classQV3DPointF.html" title="3D point representation">QV3DPointF</a> &amp;v)<span class="keyword"> const</span>
<a name="l00308"></a>00308 <span class="keyword">        </span>{
<a name="l00309"></a>00309         <span class="keyword">const</span> <span class="keywordtype">double</span>    norm = <a class="code" href="classQVQuaternion.html#ac7a9049ab48eb43f9ed7ddae01b3126a" title="Gets the norm2 of the quaternion.">norm2</a>(),
<a name="l00310"></a>00310                         x = operator[](0) / norm,
<a name="l00311"></a>00311                         y = operator[](1) / norm,
<a name="l00312"></a>00312                         z = operator[](2) / norm,
<a name="l00313"></a>00313                         w = operator[](3) / norm;
<a name="l00314"></a>00314 
<a name="l00315"></a>00315         <span class="keywordflow">if</span> (v[0] == 0 and v[1] == 0 and v[2] == 0)
<a name="l00316"></a>00316                 <span class="keywordflow">return</span> v;
<a name="l00317"></a>00317 
<a name="l00318"></a>00318 <span class="comment">//      std::cout &lt;&lt; &quot;q1&quot; &lt;&lt; std::endl;</span>
<a name="l00319"></a>00319         <span class="keyword">const</span> <a class="code" href="classQVQuaternion.html" title="Implementation of quaternions.">QVQuaternion</a> q(x, y, z, w);
<a name="l00320"></a>00320 <span class="comment">//      std::cout &lt;&lt; &quot;q2&quot; &lt;&lt; std::endl;</span>
<a name="l00321"></a>00321         <span class="keyword">const</span> <a class="code" href="classQVQuaternion.html" title="Implementation of quaternions.">QVQuaternion</a> p(v[0], v[1], v[2], 0);
<a name="l00322"></a>00322 <span class="comment">//      std::cout &lt;&lt; &quot;q3&quot; &lt;&lt; std::endl;</span>
<a name="l00323"></a>00323         <span class="keyword">const</span> <a class="code" href="classQVQuaternion.html" title="Implementation of quaternions.">QVQuaternion</a> product = q * p * q.<a class="code" href="classQVQuaternion.html#abce39f61e6deb9ca1fdab9a3745c0383" title="Gets the conjugate of the quaternion.">conjugate</a>();
<a name="l00324"></a>00324 <span class="comment">//      std::cout &lt;&lt; &quot;q4&quot; &lt;&lt; std::endl; </span>
<a name="l00325"></a>00325 
<a name="l00326"></a>00326         <a class="code" href="classQVVector.html" title="Implementation of numerical vectors.">QVVector</a> result(3);
<a name="l00327"></a>00327         result[0] = product[0];
<a name="l00328"></a>00328         result[1] = product[1];
<a name="l00329"></a>00329         result[2] = product[2];
<a name="l00330"></a>00330 
<a name="l00331"></a>00331         Q_WARNING(not result.<a class="code" href="classQVVector.html#a29235517605f49f2327df62d5e0295df" title="Checks whether the vector contains a NaN value or not.">containsNaN</a>());
<a name="l00332"></a>00332 
<a name="l00333"></a>00333         <span class="keywordflow">return</span> result;
<a name="l00334"></a>00334         }
<a name="l00335"></a>00335 
<a name="l00337"></a>00337 
<a name="l00338"></a>00338 std::ostream&amp; operator &lt;&lt; ( std::ostream &amp;os, <span class="keyword">const</span> <a class="code" href="classQVQuaternion.html" title="Implementation of quaternions.">QVQuaternion</a> &amp;quaternion )
<a name="l00339"></a>00339         {
<a name="l00340"></a>00340         <span class="keyword">const</span> <span class="keywordtype">int</span> size = quaternion.size();
<a name="l00341"></a>00341 
<a name="l00342"></a>00342         os &lt;&lt; <span class="stringliteral">&quot;QVQuaternion [&quot;</span>;
<a name="l00343"></a>00343 
<a name="l00344"></a>00344         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; size; i++)
<a name="l00345"></a>00345                 os &lt;&lt; qPrintable(QString(<span class="stringliteral">&quot;%1&quot;</span>).arg(quaternion[i], -8, <span class="charliteral">&#39;f&#39;</span>, 6)) &lt;&lt; <span class="stringliteral">&quot; &quot;</span>;
<a name="l00346"></a>00346 
<a name="l00347"></a>00347         os &lt;&lt; <span class="stringliteral">&quot;]&quot;</span> &lt;&lt; std::endl;
<a name="l00348"></a>00348         <span class="keywordflow">return</span> os;
<a name="l00349"></a>00349         }
<a name="l00350"></a>00350 
</pre></div></div>
</td></tr></table>

<br /><hr><br />
<center><a href="http://perception.inf.um.es/QVision">QVision framework</a>.
<a href="http://perception.inf.um.es">PARP research group</a>.
Copyright &copy; 2007, 2008, 2009, 2010, 2011.</center>
<br />
</body>
</html>
